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Unformatted text preview: ENEE 241 02* HOMEWORK ASSIGNMENT 30 Due Mon 04/28 Each of the infinite sequences x = x [ ], y = y [ ] and u = u [ ] (shown below) contains seven nonzero terms. 1 3 x n = 0 2 4 1 3 y n = 0 2 4 1 3 u n = 0 2 4 (i) (3 pts.) Express u [ ] as a linear combination of seven time-shifted impulses [ - m ]. (ii) (2 pts.) Express each of x [ ] and y [ ] in terms of u [ ]. (iii) (3 pts.) Express each of X ( e j ) and Y ( e j ) in terms of U ( e j ). Write down the expressions for | X ( e j ) | and | Y ( e j ) | in terms of | U ( e j ) | . How are X ( e j ) and Y ( e j ) related to U ( e j )? (iv) (4 pts.) In MATLAB notation, define a column vector a such that the command fft(a) (alone) generates U ( e j ) at 1,024 equally spaced frequencies in [0 , 2 ). Repeat for X ( e j ) and Y ( e j ). (v) (4 pts.) Express U ( e j ) in the form U ( e j ) = e- jm F ( ) , where F ( ) is a real-valued sum of cosines....
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This note was uploaded on 03/21/2010 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.
- Spring '08